Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×#11743057 |
| Fitting | C22×C7×C22⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ C2×#3535 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D7 |
| commutator, cosocle | C22×C7 | C26 |
| Frattini | C22 | C25×D7 |
| Fitting | C22×C7×C22⋊Q8 | C2 |
| socle | C23×C7 | C25 |
| hypercenter | C22×C22⋊Q8 | D7 |
| hypocenter | C7 | C2×#3535 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊Q8 | |
7302 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 1076769);